WordGPT

Solve x² + 6x + 9 = 0

The solution of x² + 6x + 9 = 0 is x = -3 (a repeated root).

x² +x += 0
x2+6x+9=0⇒x=−3x^2 + 6x + 9 = 0 \Rightarrow x = -3
Discriminant D = 0 · x ≈ -3

Change a, b or c (whole numbers, a not 0) and the exact solutions follow.

Explain it step by step in chatMake a short video of it
Graph of y = x² + 6x + 9-5.5-5-4.5-4-3.5-3-2.5-2-1.5-1-0.5123456x = -3vertexy = x² + 6x + 9
Graph of y = x² + 6x + 9. The curve crosses the x-axis at x = -3; the vertex is at (-3, 0).

How to work it out

  1. 1

    Write it in standard form a x² + b x + c = 0 and read off the coefficients: a = 1, b = 6, c = 9.

    x2+6x+9=0x^2 + 6x + 9 = 0
  2. 2

    Work out the discriminant D = b² − 4ac. Its sign tells you how many real solutions there are.

    D=62−4⋅1⋅9=36−36=0D = 6^2 - 4\cdot1\cdot9 = 36 - 36 = 0
  3. 3

    D is zero, so there is exactly one solution (a repeated root).

  4. 4

    Method 1, factoring. The roots are rational, so the left side factors:

    (x+3)(x+3)=0\left(x + 3\right)\left(x + 3\right) = 0
  5. 5

    A product is zero when one of its factors is zero, so set each factor equal to 0 and solve:

    x+3=0⇒x=−3x + 3 = 0 \Rightarrow x = -3
  6. 6

    Method 2, The quadratic formula works for every quadratic:

    x=−b±D2a=−6±02x = \frac{-b \pm \sqrt{D}}{2a} = \frac{-6 \pm \sqrt{0}}{2}
  7. 7

    Simplify to get the solution:

    x=−3x = -3
  8. 8

    Check by putting x = -3 back in: a·x² + b·x + c = 1·(9) + 6·(-3) + 9 = 0 ✓

LaTeX source of the formulas on this page
\[ x^2 + 6x + 9 = 0\ \Rightarrow\ x = -3 \]
\[ x^2 + 6x + 9 = 0 \]
\[ D = 6^2 - 4\cdot1\cdot9 = 36 - 36 = 0 \]
\[ \left(x + 3\right)\left(x + 3\right) = 0 \]
\[ x + 3 = 0 \Rightarrow x = -3 \]
\[ x = \frac{-b \pm \sqrt{D}}{2a} = \frac{-6 \pm \sqrt{0}}{2} \]
\[ x = -3 \]

The parabola y = x² + 6x + 9

xy
-69
-54
-41
-30
-21
-14
09

Questions

What are the solutions of x² + 6x + 9 = 0?

The solution of x² + 6x + 9 = 0 is x = -3 (a repeated root).

Does x² + 6x + 9 = 0 factor?

Yes: (x+3)(x+3) = 0.

What is the vertex of y = x² + 6x + 9?

(-3, 0). The parabola opens upwards, so this is the minimum.

What are the sum and product of the roots?

Sum = −b/a = -6, product = c/a = 9.

Similar equations

    Solve x² + 6x + 9 = 0: x = -3 (steps) | WordGPT